Use your fingers to gently pull the skin from the breast, legs, and thighs of the Cornish game hen without tearing the skin. Slip the truffle slices under the skin, covering the breast and legs completely. Shake a small amount of salt and pepper inside the game hen before trussing it tightly with kitchen string. Wrap the hen in plastic and refrigerate overnight to allow the truffles to flavor the meat.

Rub 1/2 tablespoon butter on the outside of the bird, then cover with salt and pepper. Rub the cut side of the garlic and then the remaining butter on the inside a small casserole just large enough to hold the bird (casserole should have a lid). Place the hen in the casserole and add the Madeira and cognac. Cover tightly and bake for 1 hour or until golden brown.